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On the determination of divergence and curl from graphical representations.

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Title: On the determination of divergence and curl from graphical representations.
Authors: Poljak, Nikola1 (AUTHOR) npoljak.phy@pmf.hr, Dulčić, Antonije1 (AUTHOR), Milin, Matko1 (AUTHOR), Požek, Miroslav1 (AUTHOR)
Source: European Journal of Physics. Jul2025, Vol. 46 Issue 4, p1-16. 16p.
Subjects: Vector calculus, Vectors (Calculus), Fluid dynamics, Electromagnetism, Intuition
Abstract: The divergence and curl operators are fundamental mathematical tools introduced in university-level electromagnetism courses. Although students generally understand the operational use of these concepts, developing a clear physical intuition of what divergence and curl are can be challenging. This difficulty often arises due to the superficial or confusing treatment found in many standard textbooks. The goal of this article is to provide a clear demonstration, based on examples, that two-dimensional visualizations can be misleading when used to interpret these operators. A combination of graphical and analytical (symbolic) representations was found to be essential for developing an accurate physical intuition about divergence and curl. A deeper comprehension of these operators not only improves proficiency in electromagnetism, but also benefits a range of other fields, from fluid dynamics to meteorology and to technical applications. [ABSTRACT FROM AUTHOR]
Copyright of European Journal of Physics is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 186412360
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: On the determination of divergence and curl from graphical representations.
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  Data: <searchLink fieldCode="JN" term="%22European+Journal+of+Physics%22">European Journal of Physics</searchLink>. Jul2025, Vol. 46 Issue 4, p1-16. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Vector+calculus%22">Vector calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Vectors+%28Calculus%29%22">Vectors (Calculus)</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+dynamics%22">Fluid dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Electromagnetism%22">Electromagnetism</searchLink><br /><searchLink fieldCode="DE" term="%22Intuition%22">Intuition</searchLink>
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  Data: The divergence and curl operators are fundamental mathematical tools introduced in university-level electromagnetism courses. Although students generally understand the operational use of these concepts, developing a clear physical intuition of what divergence and curl are can be challenging. This difficulty often arises due to the superficial or confusing treatment found in many standard textbooks. The goal of this article is to provide a clear demonstration, based on examples, that two-dimensional visualizations can be misleading when used to interpret these operators. A combination of graphical and analytical (symbolic) representations was found to be essential for developing an accurate physical intuition about divergence and curl. A deeper comprehension of these operators not only improves proficiency in electromagnetism, but also benefits a range of other fields, from fluid dynamics to meteorology and to technical applications. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of European Journal of Physics is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1088/1361-6404/addc1e
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        Text: English
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      – SubjectFull: Vector calculus
        Type: general
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      – SubjectFull: Fluid dynamics
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              M: 07
              Text: Jul2025
              Type: published
              Y: 2025
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